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We introduce a novel neural network-based PDEs solver for forward and inverse problems. The solver is grid free, mesh free, and shape free, and the solution is approximated by a neural network. We ...

The study addresses the question of whether there is a global pattern of terror organization (TO) lifespan. Based on two datasets which include hundreds of organizations, we show that there is a gl...

Support often fails to lead to beneficial results. One personality factor which may differentiate between individuals’ responses to support is an excessive sense of relational entitlement (SRE; the perception of what one deserves within a romantic relationship). We examined SRE as a moderator of the association between support matching and daily perceived partner responsiveness (PPR). We found overall positive effects for support matching, negative effects for underprovision, and limited effects for overprovision. We also found that men (but not women) with an excessive SRE experienced a greater increase in their PPR when their supportive needs were met; additionally, both men and women with an excessive SRE experienced a greater decrease in PPR when their supportive needs were not met.

Angular double-pulsed-field gradient (d-PFG) MR methodology is increasingly used to non-invasively obtain pore sizes in opaque chemical and biological systems. In such MR experiments, the angular dependency of the signal at zero mixing time, through modeling, can be used to extract the pore size. In many systems not only the pore sizes but also their directions are of importance. Before applying d-PFG NMR to complex systems, it is of value to challenge the ability of the methodology to extract these microstructural parameters in samples where the ground truth is known. In the present study we explored whether modeling of the signal in angular d-PFG NMR experiments at zero mixing time, can simultaneously provide the size and the direction of tilted compartments with little prior knowledge. We showed that the angular d-PFG MR methodology enables simultaneous extraction of the pore size and the direction of mono-dispersed phantoms and of phantoms where the restricted compartments have different pore sizes. However, we found that in phantoms with two or more pore sizes, only averaged pore sizes were extracted for large azimuthal and polar angles.

By the multiple correlation function (MCF) formalism, the nuclear magnetic resonance magnetization of diffusing spins can be represented for simple pore geometries. It may be used to infer geometric structure at the scale of microns. This is to be compared to the diffusion tensor imaging, which provides geometric information at the scale of millimeters. The MCF formulation was derived to special cases in which the gradients of the magnetic field are oriented in specific directions. A generalized approach allowing an arbitrary magnetic field direction was introduced by Ozarslan. In this article, we present a complete account of the generalized MCF mathematical derivation starting from Bloch–Torrey equations. It is aimed to the experts and novices alike. We present two approaches—the indirect derivation is based on Ozarslan's work, where the standard MCF equations are adopted to arbitrary gradient directions. Our alternative approach is based on direct calculations of the MCF matrices for specified gradient directions. We prove that the two approaches lead to the same equations. Finally, we revise Mitra's microscopic approach and show the relation to the macroscopic MCF approach. We prove that in some limit conditions the two signal equations coincide © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 16–53, 2015.

We address the problem of blind piecewise space-variant image deblurring where only part of the image is sharp, assuming a shallow depth of field which imposes significant defocus blur.

Purpose To evaluate the ability of angular double-pulsed-field gradient (d-PFG) MR to provide microstructural information in complex phantoms and fixed nerves. Methods We modeled the signal in angular d-PFG MR experiments performed on phantoms of increasing complexity where the ground truth is known a priori. After analyzing the microstructural features of such phantoms the same methodology was used to study microstructural features in fixed nerves. Results We found that our modeling is able to determine with high accuracy and with very little prior knowledge the sizes and relative fractions of the restricted components as well as the fraction of the free diffusing water molecules. The same approach was used to study nerve microstructure. We found the apparent averaged axonal diameter (AAD) to be 2.3 ± 0.2 μm. However, here the results depended, to some extent, on the parameters used to collect the data and were affected by the diffusion time. Conclusion Modeling of the angular d-PFG MR signal provides a means to obtain accurate microstructural information in complex phantoms where the ground truth is known. This approach also seems to be suitable for obtaining microstructural features in fixed nerves. Magn Reson Med 74:25–32, 2015. © 2014 Wiley Periodicals, Inc.

Diffusion NMR is a powerful tool for gleaning microstructural information on opaque systems. In this work, the signal decay in single-pulsed-field gradient diffusion NMR experiments performed on a series of phantoms of increasing complexity, where the ground truth is known a priori, was modeled and used to identify microstructural features of these complex phantoms. We were able to demonstrate that, without assuming the number of components or compartments, the modeling can identify the number of restricted components, detect their sizes with an accuracy of a fraction of a micrometer, determine their relative populations, and identify and characterize free diffusion when present in addition to the components exhibiting restricted diffusion. After the accuracy of the modeling had been demonstrated, this same approach was used to study fixed nerves under different experimental conditions. It seems that this approach is able to characterize both the averaged axon diameter and the relative population of the different diffusing components in the neuronal tissues examined.

Conventional diffusion MRI methods are mostly capable of portraying microarchitectural elements such as fiber orientation in white matter from detection of diffusion anisotropy, which arises from the coherent organization of anisotropic compartments. Double-pulsed-field-gradient MR methods provide a means for obtaining microstructural information such as compartment shape and microscopic anisotropies even in scenarios where macroscopic organization is absent. Here, we apply angular double-pulsed-gradient-spin-echo MRI in the rat brain both ex vivo and in vivo for the first time. Robust angular dependencies are detected in the brain at long mixing time (t(m) ). In many pixels, the oscillations seem to originate from residual directors in randomly oriented media, i.e., from residual ensemble anisotropy, as corroborated by quantitative simulations. We then developed an analysis scheme that enables one to map of structural indices such as apparent eccentricity (aE) and residual phase (φ) that enables characterization of the rat brain in general, and especially the rat gray matter. We conclude that double-pulsed-gradient-spin-echo MRI may in principle become important in characterizing gray matter morphological features and pathologies in both basic and applied neurosciences.

In this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation. A geodesic path is defined as the family of shapes such that the total amount of viscous dissipation caused by an optimal material transport along the path is minimized. The approach can easily be generalized to shapes given as segment contours of multi-labeled images and to geodesic paths between partially occluded objects. The proposed computational framework for finding such a minimizer is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1---1 correspondence along the induced flow in shape space. When decreasing the time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the underlying shape space. If the constraint of pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, one obtains for decreasing time step size an optical flow term controlling the transport of the shape by the underlying motion field. The method is implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations. The numerical relaxation of the energy is performed via an efficient multi-scale procedure in space and time. Various examples for 2D and 3D shapes underline the effectiveness and robustness of the proposed approach.

Image restoration, i.e., the recovery of images that have been degraded by blur and noise, is a challenging inverse problem. A unified variational approach to edge-preserving image deconvolution and impulsive noise removal has recently been suggested by the authors and shown to be effective. It leads to a minimization problem that is iteratively solved by alternate minimization for both the recovered image and the discontinuity set. The variational formulation yields a nonlinear integro-differential equation. This equation was linearized by fixed point iteration. In this paper, we analyze and prove the convergence of the iterative method.

Consider the problem of image deblurring in the presence of impulsive noise. Standard image deconvolution methods rely on the Gaussian noise model and do not perform well with impulsive noise. The main challenge is to deblur the image, recover its discontinuities and at the same time remove the impulse noise. Median-based approaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is difficult in current gradient-based edge-preserving restoration methods. The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view. We present a unified variational approach to image deblurring and impulse noise removal. The objective functional consists of a fidelity term and a regularizer. Data fidelity is quantified using the robust modified L 1 norm, and elements from the Mumford-Shah functional are used for regularization. We show that the Mumford-Shah regularizer can be viewed as an extended line process. It reflects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diffusion. This allows to distinguish outliers from edges and leads to superior experimental results.

Image restoration and segmentation are both classical problems, that are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved together. Mutual support of image restoration and segmentation processes within a joint variational framework is theoretically motivated, and validated by successful experimental results. The proposed variational method integrates semi-blind image deconvolution (parametric blur-kernel), and Mumford-Shah segmentation. The functional is formulated using the /spl Gamma/-convergence approximation and is iteratively optimized via the alternate minimization method. While the major novelty of this work is in the unified treatment of the semi-blind restoration and segmentation problems, the important special case of known blur is also considered and promising results are obtained.

To evaluate the ability of angular double-pulsed-field gradient (d-PFG) MR to provide microstructural information in complex phantoms and fixed nerves.We modeled the signal in angular d-PFG MR experiments performed on phantoms of increasing complexity where the ground truth is known a priori. After analyzing the microstructural features of such phantoms the same methodology was used to study microstructural features in fixed nerves.We found that our modeling is able to determine with high accuracy and with very little prior knowledge the sizes and relative fractions of the restricted components as well as the fraction of the free diffusing water molecules. The same approach was used to study nerve microstructure. We found the apparent averaged axonal diameter (AAD) to be 2.3 ± 0.2 μm. However, here the results depended, to some extent, on the parameters used to collect the data and were affected by the diffusion time.Modeling of the angular d-PFG MR signal provides a means to obtain accurate microstructural information in complex phantoms where the ground truth is known. This approach also seems to be suitable for obtaining microstructural features in fixed nerves. Magn Reson Med 74:25-32, 2015. © 2014 Wiley Periodicals, Inc.

Diffusion NMR is a powerful tool for gleaning microstructural information on opaque systems. In this work, the signal decay in single-pulsed-field gradient diffusion NMR experiments performed on a series of phantoms of increasing complexity, where the ground truth is known a priori, was modeled and used to identify microstructural features of these complex phantoms. We were able to demonstrate that, without assuming the number of components or compartments, the modeling can identify the number of restricted components, detect their sizes with an accuracy of a fraction of a micrometer, determine their relative populations, and identify and characterize free diffusion when present in addition to the components exhibiting restricted diffusion. After the accuracy of the modeling had been demonstrated, this same approach was used to study fixed nerves under different experimental conditions. It seems that this approach is able to characterize both the averaged axon diameter and the relative population of the different diffusing components in the neuronal tissues examined.

The left-right asymmetry in the potential amplitude on the scalp was studied in poststroke patients by using flash visual evoked potential (VEP) and a numerical two-dimensional model of the head. The left-right asymmetry of the VEP was measured in three patients after thrombosis, in one after hemorrhage, and in one healthy subject. The numerical model used computed tomography images to define the different compartments of the head. The volume conductor equation for the potential distribution created by a dipole source in the occipital region was solved numerically with use of a finite volume method. Left-right asymmetry was calculated with several values of conductivity of the damaged region. The experimental results revealed a negative asymmetry in the three patients after thrombosis (i.e., the potential amplitude over the ischemic hemisphere was smaller than that over the intact hemisphere), whereas, in the patient after hemorrhage, a positive asymmetry was found. Nonsignificant left-right asymmetry was found in the healthy subject. The numerical model revealed that the electrical conductivity of the damaged tissue has a major effect on the left-right asymmetry. Negative asymmetry, such as that found for patients after thrombosis, was obtained when the conductivity of the damaged region was greater than that of the brain, whereas positive asymmetry (hemorrhage patient) was obtained when that conductivity was smaller than that of the brain. This finding indicates that the left-right asymmetry in the scalp VEP of patients after brain damage may be a result of changes in the conductivity of the volume conductor (the ischemic region) between the source and the electrodes.

article NMR diffusion-diffraction patterns observed in compartments in which restricted diffusion occurs are a useful tool for direct extraction of compartment sizes. Such diffusion-diffraction patterns may be observed when the signal intensity E(q,Δ) is plotted against the wave-vector q (when q=(2π) −1 γδG). However, the smaller the compartment sizes are, the higher are the q-values needed to observe such diffractions. Moreover, these q-values should be achieved using short gradient pulses requiring extremely strong gradient systems. The angular double-pulsed-field gradient (d-PFG) NMR methodology has been proposed as a tool to extract compartment sizes using relatively low q-values. In this study, we have used single-PFG (s-PFG) NMR and angular d-PFG NMR to characterize the size of microcapillaries of about 2±1 μm in diameter. We found that these microcapillaries are characterized by relatively strong background gradients that completely masked the effects of the microscopic anisotropy (μA) of the sample, resulting in a completely unexpected E(φ )p rofile in the angular d-PFG NMR experiments. We also show that bipolar angular d-PFG NMR experiments can largely suppress the effect of these background gradients resulting in the expected E(φ) profile from which the compartment dimensions could be obtained with relatively weak gradient pulses. These results demonstrate that the above methodology provides a quick, reliable, non-invasive means for estimating small pore sizes with relatively weak gradients in the presence of large magnetic susceptibility.

We present in this paper a unifying generalization of the Mumford-Shah functional, in the Ambrosio-Totorelli set up, and the Beltrami framework. The generalization of the Ambrosio-Tortorelli is in using a diffusion tensor as an indicator of the edge set instead of a function. The generalization of the Beltrami framework is in adding a penalty term on the metric such that it is defined dynamically from minimization of the functional. We show that we are able, in this way, to have the benefits of true anisotropic diffusion together with a dynamically tuned metric/diffusion tensor. The functional is naturally defined in terms of the vielbein-the metric's square root. Preliminary results show improvement on both the Beltrami flow and the Mumford-Shah flow.

Sparse representation theory has been increasingly used in the fields of signal processing and machine learning. The standard sparse models are not invariant to spatial transformations such as image rotations, and the representation is very sensitive even under small such distortions. Most studies addressing this problem proposed algorithms which either use transformed data as part of the training set, or are invariant or robust only under minor transformations. In this paper we suggest a framework which extracts sparse features invariant under significant rotations and scalings. The algorithm is based on a hierarchical architecture of dictionary learning for sparse coding in a cortical (log-polar) space. The proposed model is tested in supervised classification applications and proved to be robust under transformed data.

A variational approach to defining geodesics in the space of implicitly described shapes is introduced in this paper. The proposed framework is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1-1 property of the induced flow in shape space. For decreasing time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the shape space. Considering shapes as boundary contours, the proposed shape metric is identical to a physical dissipation in a viscous fluid model of optimal transportation. If the pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, for decreasing time step size one obtains an additional optical flow term controlling the transport of the shape by the underlying motion field. The implementation of the proposed approach is based on a level set representation of shapes, which allows topological transitions along the geodesic path. For the spatial discretization a finite element approximation is employed both for the pairwise deformations and for the level set representation. The numerical relaxation of the energy is performed via an efficient multi---scale procedure in space and time. Examples for 2D and 3D shapes underline the effectiveness and robustness of the proposed approach.

Many problems in image processing are solved via the minimization of a cost functional. The most widely used optimization technique is the gradient descent, often used due to its simplicity and applicability where other optimization techniques, e.g., those coming from discrete optimization, can not be used. Yet, gradient descent suffers from a slow convergence, and often to just local minima which highly depends on the condition number of the functional Hessian. Newton- type methods, on the other hand, are known to have a rapid (quadratic) convergence. In its classical form, the Newton method relies on the L2-type norm to define the descent direction. In this paper, we generalize and reformulate this very important optimization method by introducing a novel Newton method based on general norms. This generalization opens up new possibilities in the extraction of the Newton step, including benefits such as mathematical stability and smoothness constraints. We first present the derivation of the modified Newton step in the calculus of variation framework. Then we demonstrate the method with two common objective functionals: variational image deblurring and geodesic active contours. We show that in addition to the fast convergence, different selections norm yield different and superior results.